Table of Contents
Preface xi
Chapter 1 Concepts from Probability Theory and Statistics 1
1.1 The role of probability in civil engineering 1
1.2 Physical and statistical uncertainties 2
1.3 Axiomatics 3
1.3.1 Probabilities 3
1.3.2 Axioms 3
1.3.3 Consequences 5
1.3.4 Conditional probabilities 5
1.4 Random variables - distributions 8
1.4.1 Definitions 8
1.4.2 Sampling 8
1.4.3 Probability density function 10
1.4.4 Main descriptors of a random variable 11
1.4.5 Joint variables 15
1.4.6 Independent variables 16
1.4.7 Correlation coefficient 16
1.4.8 Functions of random variables 18
1.4.9 Approximate moments 20
1.5 Useful random variables 21
1.5.1 Discrete variables 21
1.5.2 Normal distribution 25
1.5.3 Lognormal distribution 26
1.5.4 Beta distribution 28
1.5.5 Exponential distribution 29
1.5.6 Gamma distribution 30
1.5.7 tudent's t-distribution 31
1.6 Limit theorems 31
1.6.1 Law of large numbers 32
1.6.2 Limit theorems 35
1.7 Modeling random variables 38
1.7.1 Point estimation 39
1.7.2 Interval estimation 43
1.7.3 Estimation of fractiles 46
1.7.4 Estimation of the distribution 48
1.8 Distribution of extremes 51
1.9 Significance testing 58
1.9.1 Type I and II errors 60
1.9.2 Usual tests 61
1.10 Bayesian analysis 65
1.10.1 A priori and a posteriori distributions 66
1.10.2 Updating estimators 68
1.10.3 Bayesian networks 70
1.11 Stochastic processes 74
1.11.1 Basic principles 74
1.11.2 Markovian chains 75
1.11.3 State probability 76
1.11.4 Time between stages 78
Chapter 2 Structural Safety, Performance and Risk 81
2.1 Introduction 81
2.2 Safety and risk 82
2.2.1 Concepts of safety 82
2.2.2 Concept of risk related to a danger or threat 83
2.2.3 Risk assessment 84
2.2.4 Hazard 85
2.3 Risk evaluation and acceptable risk 87
2.3.1 Risk assessment 87
2.3.2 Acceptable risk 89
2.4 Risk-based management 96
2.4.1 Strategies 96
2.4.2 Risk analysis 96
2.4.3 Legal point of view for a risk-based approach 104
2.5 Examples of failure: bridges 105
2.6 From safety to performance 110
2.6.1 Functions of a structure 110
2.6.2 Performance 112
2.6.3 Evolution of structural functionality 119
2.6.4 Consequences of performance losses 121
2.6.5 Generalization of the concept of risk 121
2.7 Human errors 122
Chapter 3 Performance-based Assessment 125
3.1 Analysis methods and structural safety 125
3.1.1 Allowable stress principle 128
3.1.2 Limit states and partial factors 128
3.1.3 Probability-based approach 132
3.2 Safety and performance principles 134
3.2.1 New structures 135
3.2.2 Existing structures 135
3.3 Invariant measures 136
3.4 Reliability theory 138
3.4.1 Basic problem 138
3.4.2 Convolution integral 139
3.4.3 Normal variables 140
3.4.4 Geometric expression of the reliability index 142
3.4.5 Joint distribution representation 145
3.4.6 Limit state with more than two uncorrelated normal variables 145
3.4.7 Limit state with correlated variables 148
3.5 General formulation 150
3.5.1 Failure component-failure mode 150
3.5.2 Safety margins - limit state functions 150
3.5.3 Calculation methods 151
3.5.4 Basler-Cornell index 152
3.5.5 Hasofer-Lind index 158
3.5.6 Rackwitz-Fiessler algorithm 161
3.5.7 Isoprobability transformations 162
3.5.8 Calculation of the failure probability 168
3.5.9 Monte-Carlo methods 172
3.5.10 Response surfaces 176
3.5.11 Sensitivity measures 183
3.6 System reliability 187
3.6.1 Mathematical concepts 190
3.6.2 Calculation of the system probability of failure 199
3.6.3 Robustness and vulnerability 205
3.7 Determination of collapse/failure mechanisms 208
3.7.1 Generation of safety margins for truss structures 208
3.7.2 P-unzipping method 213
3.8 Calibration of partial factors 217
3.9 Nature of a probabilistic calculation 224
3.10 Failure probabilities and acceptable risks 225
3.10.1 Acceptable failure probabilities 225
3.10.2 Concept of acceptable risk 230
3.10.3 Remarks 233
Chapter 4 Structural Assessment of Existing Structures 235
4.1 Introduction 235
4.2 Assessment rules 236
4.3 Limits when using design rules 236
4.4 Main stages in structural assessment 237
4.5 Structural safety assessment 239
4.5.1 Basic concept 240
4.5.2 First approach 240
4.5.3 Second approach 242
4.5.4 Third approach 244
4.5.5 Fourth approach 250
4.5.6 Implementing rating factors 258
4.6 General remarks on the methods 260
Chapter 5 Specificities of Existing Structures 261
5.1 Loads 261
5.1.1 Introduction 261
5.1.2 Stochastic processes 264
5.1.3 Spatial variability 285
5.1.4 Load combinations 286
5.1.5 Permanent loads 288
5.1.6 Live loads 291
5.1.7 Environmental loads 298
5.1.8 Exceptional loads 325
5.2 Resistance 331
5.2.1 Material properties and uncertainties 332
5.2.2 Properties of reinforcing and prestressing steel 334
5.2.3 properties of structural steel 340
5.2.4 Properties of concrete 341
5.3 Geometric variability 348
5.4 Scale effects 351
Chapter 6 Principles of Decision Theory 355
6.1 Introduction 355
6.2 The decision model 356
6.2.1 Decision tree 356
6.2.2 Decision criterion 360
6.2.3 Terminal decision analysis 361
6.2.4 Information value 363
6.3 Controls and inspections 364
6.3.1 Detection probability: a discrete case 367
6.3.2. Detection probability: a continuous case 375
6.3.3 Load tests 381
6.4 Maintenance optimization 384
6.4.1 Identification of degradations and failure modes 387
6.4.2 Decision process and RBI analysis 389
6.4.3 Maintenance types 390
6.5 Life cycle cost analysis 391
6.5.1 Discount calculations 392
6.5.2 Discount rate 394
6.5.3 Some results from discounting analysis 396
6.5.4 Condition, working lifetime and life cycles 398
6.6 Maintenance strategies 403
6.6.1 Corrective maintenance 404
6.6.2 Systematic maintenance 405
6.6.3 Conditional maintenance 406
Bibliography 413
Index 423
